Open Access
August 2010 Functional linear regression via canonical analysis
Guozhong He, Hans-Georg Müller, Jane-Ling Wang, Wenjing Yang
Bernoulli 16(3): 705-729 (August 2010). DOI: 10.3150/09-BEJ228


We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression models and some basic properties are explored for this situation. We derive a representation of the regression parameter function in terms of the canonical components of the processes involved. This representation establishes a connection between functional regression and functional canonical analysis and suggests alternative approaches for the implementation of functional linear regression analysis. A specific procedure for the estimation of the regression parameter function using canonical expansions is proposed and compared with an established functional principal component regression approach. As an example of an application, we present an analysis of mortality data for cohorts of medflies, obtained in experimental studies of aging and longevity.


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Guozhong He. Hans-Georg Müller. Jane-Ling Wang. Wenjing Yang. "Functional linear regression via canonical analysis." Bernoulli 16 (3) 705 - 729, August 2010.


Published: August 2010
First available in Project Euclid: 6 August 2010

zbMATH: 1220.62076
MathSciNet: MR2730645
Digital Object Identifier: 10.3150/09-BEJ228

Keywords: canonical components , Covariance operator , Functional data analysis , functional linear model , longitudinal data , parameter function , stochastic process

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

Vol.16 • No. 3 • August 2010
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